In this study a new method for design optimization is proposed that is based on "transfer learning". The proposed framework improves the accuracy and efficiency of surrogate-based optimization. A surrogate model is an approximation to a costly black-box function that can be used for more efficient search of optimal points. When design specifications change, the objective function changes too. Therefore, there is a need for a new surrogate model. However, the concept of transfer learning can be applied to refit the new surrogate more efficiently. In other words insights from previous experiences can be applied to learning and optimizing the new function. We use the proposed method in a particular problem pertaining to the design of "thin film multilayer solar cells", where the goal is to maximize the external quantum efficiency of photoelectric conversion. The results show that the accuracy of the surrogate model is improved by 2-3 times using the transfer learning approach, using only half as many training data points as the original model. In addition, by transferring the design knowledge from one particular set of materials to another similar set of materials in the thin film structure, the surrogate-based optimization is improved, and is it obtained with far less computational time.